We observe first that it follows from (REF ) that \(f\)  is bounded on \([0,1]\) . Consequently, to show that \(f\)  is convex on \([0,1]\) , it suffices to show that \(f\)  is mid-point convex. See, for example, [1]}, Chapter 5, 25.3. To this end, suppose that \(t\pm s\in [0,1]\)  and
using  (REF ), observe that

 atxb1-trE()2
= as(at-sxb1-t-s)bsrE()2
